Question

If Logx (1 / 8) = - 3 / 2, then x is equal to
A. - 4
B. 4
C. 1 / 4
D. 10

Answer 1

C 1/4

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Answer 2

Answer:

x=4

Step-by-step explanation:

$log_{x}( \frac{1}{8} ) = \frac{ - 3}{2}$

So,

$log_{x}( {( \frac{1}{2} )}^{3} ) = \frac{ - 3}{2}$

So,

$3 log_{x}( \frac{1}{2} ) = \frac{ - 3}{2}$

So,

$log_{x}( \frac{1}{2} ) = \frac{ - 1}{2}$

So,

${x}^{ \frac{ - 1}{2} } = \frac{1}{2}$

So,

$\frac{1}{ \sqrt{x} } = \frac{1}{2}$

Squaring both sides,

$\frac{1}{x} = \frac{1}{4}$

Or, x=4

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